Interaction of a dense fermion medium with a scalar-meson field

The interaction between a dense fermion medium and a scalar-meson field is studied. It is shown that in the quasiclassical approximation, independently of the details of the theory, at low fermion density the lowest energy state is normal (i.e., effective fermion mass m_eff≅free mass, but at high density the state is abnormal (i.e., m_eff≅0). The nature of the transition is analyzed at zero and low temperatures. Our main concern is to examine the problem of quantum fluctuation. Both the one- and two-loop diagrams are calculated. By developing a variational formalism involving only two-line irreducible diagrams, we derive a suitable high-density expansion for the energy. The quasiclassical solution emerges as the lowest-order term in this expansion. Therefore, when the expansion is valid, the overall description of the transition given by the quasiclassical solution remains correct with the inclusion of quantum corrections.